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arXiv · 2401.07998

Distal expansions of Presburger arithmetic by a sparse predicate

Mervyn Tong
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Abstract

We prove that the structure $(\mathbb{Z},<,+,R)$ is distal for all congruence-periodic sparse predicates $R\subseteq\mathbb{N}$. We do so by constructing strong honest definitions for representative formulas of the theory, providing a rare example of concrete distal decompositions.

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Mervyn Tong. 2024-01-15. Distal expansions of Presburger arithmetic by a sparse predicate. https://doi.org/10.1017/jsl.2025.10125

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